Question

If log 2 = 0.3010, log 3 = 0.4771 and log 7 = 0.8451, find the value of log 84.

Answer 1

Given:

log 2 = 0.3010

log 3 = 0.4771

log 7 = 0.8451

To find: Value of log 84.

Calculation:

Step 1: Express 84 as a product of primes:

84

= 7 × 12 

= 7 × (3 × 2²)

Step 2: Use the logarithmic property:

log(a × b × c) = log a + log b + log c

log 84 = log 7 + log 3 + log 2²

Now, use the logarithmic power rule for log 2²: 

log 2² = 2 log 2 

So:

log 84 = log 7 + log 3 + 2 log 2

Step 3: Substitute the given values:

Substitute log 7 = 0.8451, log 3 = 0.4771 and log 2 = 0.3010: 

log 84 = 0.8451 + 0.4771 + 2 × 0.3010

Step 4: Calculate the result:

log 84 = 0.8451 + 0.4771 + 0.6020

log 84 = 1.9242